A 64 lb object stretches a spring 4 ft. It is attached to a dashpot with damping = 8 lb-sec/ft. The object is initially displaced 12 inches above equilibrium and given a downward velocity of 4 ft/sec. Find the equation of motion. - constant y Ou(t) = 2e-2t sin (2t) Ou(t) Ou(t) - -2t = e e Ou(t)=e-2t sin (2t) -e-2t cos (2t) cos (2t) e 2t sin (2t) - =e-2t sin (2t) - 2e-2t cos (2t) -2t cos (2t)
A 64 lb object stretches a spring 4 ft. It is attached to a dashpot with damping = 8 lb-sec/ft. The object is initially displaced 12 inches above equilibrium and given a downward velocity of 4 ft/sec. Find the equation of motion. - constant y Ou(t) = 2e-2t sin (2t) Ou(t) Ou(t) - -2t = e e Ou(t)=e-2t sin (2t) -e-2t cos (2t) cos (2t) e 2t sin (2t) - =e-2t sin (2t) - 2e-2t cos (2t) -2t cos (2t)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A 64 lb object stretches a spring 4 ft. It is attached to a dashpot with damping
= 8 lb-sec/ft. The object is initially displaced 12 inches above
equilibrium and given a downward velocity of 4 ft/sec. Find the equation of motion.
=
constant y
Ou(t) = 2e-2t sin (2t)
Ou(t)= e 2t sin (2t)
Ou(t)
Ou(t)
e
-2t cos (2t)
e-2t sin (2t) - e-2t cos (2t)
-2t
= e
cos (2t) e 2t sin(2t)
-
=e-2t sin (2t) - 2e-2t cos (2t)
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